On Monday, Cora announced that catcher Kevin Plawecki and two staff members have tested positive for COVID-19.
Cora said he also expects to be without multiple unvaccinated players.
Starting pitcher Tanner Houck told The Boston Globe on Sunday that he is not vaccinated against COVID-19 and won't pitch during the four-game series beginning April 25. He would have been in line to start the second game.
To enter Canada, the Canadian government requires a person must have received a second COVID-19 vaccine dose -- or one dose of Johnson & Johnson -- at least 14 days prior to entry.
"I'm bummed that I won't be able to make that start," said Houck (1-0), who has been sharp in two starts this season, including a win over the Minnesota Twins on Saturday at Fenway Park.
Cora was asked after an 8-1 win over the Twins on Sunday whether he expected to be missing other players.
"Yeah," Cora said. He was not asked a follow-up question and then ended the news conference.
Asked earlier about Houck, Cora said: "We knew it beforehand, so we'll plan accordingly."
Players sidelined by COVID-19 vaccine issues are not paid and do not accrue major league service time while on the restricted list.
"I think it's a personal choice for everyone whether they get it or not," Houck told the Globe.
Major League Baseball is not alone in this issue with regards to travel to Canada. The Philadelphia 76ers will be without guard Matisse Thybulle when their Eastern Conference playoff series vs. the Toronto Raptors heads north for Games 3 and 4.
The Associated Press contributed to this report.